The present invention relates to methods for determining linear positioning inaccuracies of a moving member of a machine due to thermal expansion of the machine member and of the machine. More particularly, the present invention relates to a method for determining linear positioning inaccuracies of a moving member of a machine due to thermal expansion of the machine member and of the machine, wherein an effective coefficient of thermal expansion of the machine is derived empirically, and wherein such effective coefficient of thermal expansion is used to compensate for such positioning inaccuracies.
Large metal-working machines, such as, for example, gantry-style machine tools (oftentimes referred-to by those skilled in the art as “profiler machines”), are constructed largely out of structural steel. Like other materials used to construct machine members, steel possesses a metallurgical property which causes a machine member constructed therefrom to deform linearly in response to changes in its temperature. For example, a machine member of a long-travel machine tool—such as an elongate rail upon which another machine member rides—constructed out of steel and having a fixed length L, will change linearly in length due to changes in the temperature thereof an amount equal to:ΔL=L·α·ΔT  (1)where:
ΔL=a change in length of the member;
L=an initial length of the member at an initial temperature Ti thereof;
α=the coefficient of thermal expansion (“thermal coefficient”); and,
ΔT=a change in temperature of the member=Tf−Ti, where:                Tf=a temperature of the member.        
The thermal coefficient α is the rate at which a change in the length of the machine member ΔL will be directly proportional to a change in the temperature ΔT thereof and is a property of the specific material used to construct the member. Accordingly, the thermal coefficient α is used to calculate both increases in the length of a machine member due to increases in the temperature thereof, as well as decreases in the length of the machine member due to decreases in the temperature thereof. However, for the purpose of clarity and illustration, the within description will refer only to increases in the length of the machine member due to increases in the temperature thereof, although such description shall apply equally to decreases in the length of the machine member due to decreases in the temperature thereof without departing from either the spirit or the scope of the present invention.
The value of the thermal coefficient α for most materials is considered by those skilled in the art to be constant through a wide range of temperatures, including standard “room” temperature of 68° F. (20° C.), which is accepted by those skilled in the art as being a suitable (albeit generalized) baseline temperature for most thermal expansion calculations. As such, thermal expansion measurements and calculations typically are performed with reference to the initial temperature Ti of the machine member being 68° F. (20° C.). For convenience, “textbook” values of common thermal coefficients a which are based on an initial temperature of 68° F. (20° C.) are used typically in performing these calculations.
However, the “true” value of the thermal coefficient may be different from the “textbook” value thereof and thermal expansion measurements and calculations of machine members based on a “textbook” value of the thermal coefficient α may lead to inaccurate calculations, albeit generally of small magnitudes. Nevertheless, in machining operations, such as those typically performed by profiler machines, where high degrees of machining accuracy are required, even minimally inaccurate calculations may lead to significant dimensional machining errors. It is therefore desirable to provide a method for determining the “effective” value of the thermal coefficient α of a machine member. It is also desirable to provide a method for determining the “effective” value of the thermal coefficient α of a machine member, with reference to the environmental conditions surrounding it.
Machines typically are not comprised only of a single element, but rather, include combinations of numerous elements, parts, components or members which are fixedly, slidably, rotatably or otherwise operatively connected to one another to form an interrelated, operative structure For example, a profiler machine typically comprises three main sub-structures: 1) a bed upon which a workpiece is secured; 2) a head supported over the bed for positioning a cutting tool in close proximity to the workpiece for performing machining operations thereon; and, 3) a rail system for supporting the head over the bed and for providing movement of the head with respect to the bed along an elongate axis thereof. Each of the three main sub-structures includes numerous parts operatively engaging one another for performing machining operations according to a preselected design configuration, and each such part has thermal properties according to the material from which such part is constructed. As the temperature of each member increases, for example, due to an increase in the temperature of the air surrounding the machine (thereby increasing the temperature of the part itself) the members individually experience thermal expansion at a rate equal to the thermal coefficient α of the material from which the members are respectively constructed. It would not be uncommon for the parts to be constructed from different materials, in which case each material typically will have a unique thermal coefficient α, and the parts of the machine will expand at different rates leading a non-uniform expansion of the machine. It is desirable therefore to provide a method for determining an “effective” value of the thermal coefficient α of a machine comprised of members constructed of materials having differing individual thermal coefficients α.
Moreover, in a conventional machine, the members thereof are constrained from moving freely because the members are operatively connected to other machine members, as well as to support structures. For example, the rail system of a conventional profiler machine comprises a pair of elongate rails along which the head traverses. The rails are fixedly anchored to the machine shop floor by several structural bolts, thereby limiting the free thermal elongation of the rails. Because machining accuracy depends directly on the accurate positioning of the head along the rails, it is necessary to be able to calculate how the rails expand in response to increases in the temperature thereof. However, because the rails are constrained, conventional thermal expansion calculations based upon “textbook” values of the thermal coefficient α likely will not accurately predict the expansion of the rails due to increases in the temperature thereof. Accordingly, it is desirable furthermore to provide a method for determining the “effective” value of the thermal coefficient α of a machine comprised of members which are constrained from freely moving in response to changes in the temperatures thereof.
The size and geometry of conventional machine tools, such as profiler machines, oftentimes results in localized heat pockets being created at isolated locations of the machine members, thereby giving rise to localized rates of thermal expansion which are different from the rates of thermal expansion at other locations of the machine and of the machine members. That is, the temperature of the machine varies (sometimes widely) across the entire machine, making it difficult to determine where to measure the temperature of the machine, for example, for the purpose of performing “textbook” thermal expansion calculations. Accordingly, it is desirable furthermore to provide a method for determining an “effective” temperature of the machine, which such “effective temperature” thereof may be used, for example, in performing thermal expansion calculations.
It is known that machine tools must be calibrated from time-to-time to correct for mechanical and thermal positioning errors. However, while conventional machine calibration practices may adequately compensate for mechanical positioning errors, they incorporate only “textbook” values of thermal coefficients, and as such, machine compensation tables resulting therefrom do not adequately consider the unique thermal characteristics of the machine being calibrated. Accordingly, it is desirable furthermore to provide a method for calibrating a machine wherein the true thermal characteristics of the machine are closely approximated, such as, with reference to an “effective” thermal coefficient thereof. Moreover, conventional machine calibration practices do not consider the thermal characteristics of a workpiece being machined thereby. That is, machine compensation tables resulting from conventional machine calibration practices are not adapted to be modified for machining workpieces constructed out of materials having thermal characteristics differing significantly from the thermal characteristics of the machine. For example, an aluminum workpiece will expand at a rate much greater than the rate at which a profiler machine will expand and the machine compensation tables resulting from conventional machine calibration practices reflect only the thermal characteristics of the machine, which will result in machining inaccuracies unless the NC “part program” used to instruct the machine for performing machining operations is modified to account for the unique thermal characteristics of the workpiece relative to the thermal characteristics of the machine. Oftentimes, such modification must be performed manually by an NC programmer or are incorporated into so-called “post-process” modification of the NC program. It is desirable therefore to provide a method for calibrating a machine wherein the thermal characteristics of a workpiece to be machined thereby are incorporated thereinto. It is desirable even further to provide a method for calibrating a machine wherein the thermal characteristics of a workpiece to be machined thereby are incorporated thereinto, and wherein a plurality of workpiece materials may be considered.